I'm starting to think this can be a very old and small Malus sylvestris or a related one... Not sure at all, anyway... https://commons.wikimedia.org/wiki/File:Malus_sylvestris_004.JPG

whether or not it is a useful tree .. depends on your yard size.. and your garden ... and perhaps.. where you are ... if in fact.. the seed shot out of a birds butt ... that might mean its a messy tree ... and that it has the potential to be a PIA ... i have serotina all over my 5 acres ... the flowers smell like dirty gym socks .. and the bigger the tree gets.. the bigger the stink ... the fruit is useless in that the pit is 95% of the cherry .. and all its good for.. is for birds to eat and spread for a half mile around the house ... out here in the country.. the birds have plenty to eat ... i really dont see why they need these trees ... unfortunately.. i have a dozen 60 footers.. and there is nothing i can do about it ... except encourage the hate .. lol if i were on a small suburban yard ... i would be very leery about encouraging it ... its not all that expensive to buy a good heirloom tree for that purpose ... ken

Ken - it's not as simple as "the green one" vs. "the purple one." ==>>> in variegated plants... the all green one.. is usually the most vigorous.. because it has the most usable chlorophyll .... [im not talking about dwarf culitvars now] in general .. not limited to smokebush .... any amount of white in the leave.. and it usually has a lower annual growth rate ... ergo.. over ten years.. it ends up a smaller plant than the green one ... blue plants.. have a waxy coating over the green.. that makes them appear blue ... and again.. interrupts the usage of sunlight.. ergo.. they are usually smaller.. over that given decade ... and purple.. well thats just wrong... lol ... and i dont seem to recall it is green under the purple ... but regardless.. not being green.. its has the slower growth rate.. over the given time ... sooo.. the rest of my sentence implied ... that a green one would have greater potential over the years ... and i also noted its kind of jammed in that fence corner.. and lucky its the purple one ... since it will stay smaller over the given time span ... btw: if i didnt say it above.. i figure the prior owner pruned it to tree form ... because it was taking up to much floor space .... and that is just fine ... whoever owns the pruners and the plant rules .... ken

Thank you so much. So the Chinese Pistache guess is wrong. (The Chinese Pistache is the second photo - a screenshot I took while trying to identify the tree in the first, third and last pictures). I actually didn’t intend to post that screenshot at all but I can’t figure out how to remove it from the post. 🤷‍♀️ Hence the long explanation. The second photo was posted in error.